You could try and see if a replacement casement handle would work.

Oops, I just reread and think that you may be talking about the vinyl, itself, not just the protruding handle (which is a problem, by itself).

Maybe someone else knows about drilling into vinyl.

Here is a link that might be useful: handles

It'd help if you could take a closer shot, but it appears you have two different recessed areas to work around.
Is the area closest to the window frame a level surface, or am I seeing small molding there?
Either way, you should be able to drill thru the vinyl and hit
the rough framing that holds the window.

I'd first contact the manufacturer or try to find the windows locally and ask how they're installed. That will help you determine how to attach window treatments.

Not all windows allow for inside mount blinds. You could mount a blind or shade on the wood frame.

Are they just vinyl clad with wood underneath?

Do you know the make and model of the windows, so that you could check the specs?

Call the manufacturer. Different manufacturers have different insides.

I would hang roman shades or bamboo blinds into the drywall high above the window (outside mount), just at the level of a high curtain rod, combined with curtains. Make the rod wider than the window so you can pull the curtains to the side and see the whole window. Ideally the curtains go to the floor. You can see examples of this in some of the pictures on this blog about window treatments, and it looks fabulous. (warning, photo intensive link) It's about 1/3 of the way down the post, under the "curtain panels paired with blinds" section. hth

Here is a link that might be useful: Cote de Texas top ten #4, curtains

I just bought this house so I am not sure about the windows. I will see if I can find out the name and manufacturer.
In the photo I posted there are only 2 windows side by side, but some rooms have 4 going across and I was hoping for some bamboo shades or roman shades on each individual window as there would be no place to hang outside mount unless I did one huge blind.